Abstract
The phenomenon of the higher-order vagueness is one of the most controversial issues of the semantics for vagueness. Timothy Williamson has argued that any theory would inevitably fail if it aims at explicating higher-order vagueness in terms of revising classical logic, for the problem of higher-order vagueness consists not in the inadequacy of classical logic but rather in the limitation of our cognitive ability. Williamson proposes the epistemic theory and claims that it is the best option to dissolve the challenge of the phenomenon of higher-order vagueness. Nevertheless, I disagree with Williamson. In this paper, I will argue that the most promising response to the challenge of higher-order vagueness argument is supervaluationism rather than the epistemic theory. However, the orthodox supervaluationism cannot dissolve the phenomenon of higher-order vagueness because the model is static. I suggest that we should turn the static model of supervaluationism into a dynamic one, which, as I will argue, release the pressure of supervaluationism from the challenge of higher-order vagueness argument.
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Notes
- 1.
I have learned the way of this request from the anti-luminosity argument which appears in the chapter four of Timothy Williamson’s Knowledge and Its Limits.
- 2.
The name of admissible interpretations originated from Kit Fine, and he took the notion of admissibility as primitive. (Fine 1975: 272).
- 3.
The main purpose of Tye’s paper is to show that Hyde fails to demonstrate that higher-order vagueness is a real phenomenon but a pseudo one. However, it seems to me that Tye has attempted to dissolve higher-order vagueness and emphasized the importance of vaguely vague, perhaps vaguely vague. Nevertheless, the success of the position depends on the soundness of Sorenson’s argument.
- 4.
Williamson has proposed three difficulties to supervaluationism, the other two are connected to the two-valued logic. As he said, “According to supervaluationism, ‘por q’ is sometimes true when no answer to the question ‘Which?’ is true. For similar reasons, ‘Something is F’ is sometimes true when no answer to the question ‘Which thing is F?’ is true. In this sense supertruth is elusive.” (Williamson 1994, p. 153) and “Truth is standardly assumed to have the disquotational property to which Tarski drew attention. ...... Supertruth is not disquotational. If it were, then the supervaluationist would be forced to admit bivalence. Consider any sentence ‘A’. By supervaluationist logic, either Aor not A. Suppose that supertruth is disquotational. Thus ‘A’ is supertrue if and only if A and ‘Not A’ is supertrue if and only if not A. It would then follow, by more supervaluationist logic, that either ‘A’ is supertrue or ‘Not A’ is supertrue; in the latter case, ‘A’ is superfalse.”(Williamson 1994, p. 162) I would ignore these two difficulties here because they are connected the problem of semantic rules for vagueness directly.
- 5.
“Precisification” means that there is a sharp boundary between true and false in every admissible interpretation. So, let us stipulate the precisification (or in Sainsbury’s word, sharpening) s(w) of a vague predicate and the value of a sentence meets the following conditions, (Sainsbury 2009:52)
\(\bullet \) If w is definitely true of something, then s(w) is true of it.
\(\bullet \) If wis definitely false of something, then s(w) is false of it.
\(\bullet \) For each object, s(w) is either true of it or false of it.
\(\bullet \) s(w) respects the underlying ordering (if there is one). For example, if s(“tall”) is true of someone 6\(^{\prime }\) tall, it is also true of someone 6\(^{\prime }\)1\(^{\prime \prime }\).
- 6.
The phrase ‘complete and admissible specifications’ is from Keefe (2000): Chap. 8.
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Fu, HC. (2017). Saving Supervaluationism from the Challenge of Higher-Order Vagueness Argument. In: Yang, SM., Lee, K., Ono, H. (eds) Philosophical Logic: Current Trends in Asia. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-10-6355-8_7
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